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Closed mappings and quasimetrics


Author: Jacob Kofner
Journal: Proc. Amer. Math. Soc. 80 (1980), 333-336
MSC: Primary 54E15; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1980-0577769-6
MathSciNet review: 577769
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Abstract: Closed continuous mappings with first countable images preserve quasi-metric spaces as well as nonarchimedean quasi-metric spaces and $ \gamma $-spaces. This is a strict generalization of analogous results on perfect mappings: there exists a closed continuous mapping of a nonarchimedean quasi-metric Moore space onto a compact metric space which is neither perfect nor boundary compact.

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  • [B] H. R. Bennett, Quasimetrizability and the 𝛾-space property in certain generalized ordered spaces, The Proceedings of the 1979 Topology Conference (Ohio Univ., Athens, Ohio, 1979), 1979, pp. 1–12 (1980). MR 583684
  • [F] R. Fox, On metrizability and quasi-metrizability (to appear).
  • [GJ] Leonard Gillman and Meyer Jerison, Rings of continuous functions, Springer-Verlag, New York-Heidelberg, 1976. Reprint of the 1960 edition; Graduate Texts in Mathematics, No. 43. MR 0407579
  • [G] Gary Gruenhage, A note on quasi-metrizability, Canad. J. Math. 29 (1977), no. 2, 360–366. MR 0436089, https://doi.org/10.4153/CJM-1977-039-2
  • [J1] H. Junnila, Covering properties and quasi-uniformities of topological spaces, Ph. D. Thesis, Virginia Polytechnic Institute and State University, 1978.
  • [J2] Heikki J. K. Junnila, Neighbornets, Pacific J. Math. 76 (1978), no. 1, 83–108. MR 0482677
  • [K1] Ja. A. Kofner, Δ-metrizable spaces, Mat. Zametki 13 (1973), 277–287 (Russian). MR 0324664
  • [K2] -, Semi-stratifiable spaces and spaces with generalized metrices, Ph. D. Thesis, The Technion, Haifa, Israel, 1975.
  • [K3] -, Quasi-metrizable spaces, Pacific J. Math. 82 (1979).
  • [NC] S. Ĭ. Nedev and M. M. Čoban, On the theory of 𝑜-metrizable spaces. III, Vestnik Moskov. Univ. Ser. I Mat. Meh. 27 (1972), no. 3, 10–15 (Russian, with English summary). MR 0307192
  • [TP] Topology Proceedings 2 (1977), 687.
  • [V] N. V. Veličko, Quasiuniformly sequential spaces, C. R. Acad. Bulgare Sci. 25 (1972), 589–591 (Russian). MR 0305324

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0577769-6
Keywords: Closed mapping, quasi-metric, nonarchimedean quasi-metric, $ \gamma $-space, perfect mapping, first countable space
Article copyright: © Copyright 1980 American Mathematical Society

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